Problem: Solve for $x$ and $y$ using elimination. ${6x+2y = 62}$ ${5x-2y = 37}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $11x = 99$ $\dfrac{11x}{{11}} = \dfrac{99}{{11}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {6x+2y = 62}\thinspace$ to find $y$ ${6}{(9)}{ + 2y = 62}$ $54+2y = 62$ $54{-54} + 2y = 62{-54}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 9}$ into $\thinspace {5x-2y = 37}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ - 2y = 37}$ ${y = 4}$